# Simple Ratings

The Simple ratings, for rating and ranking teams according to the record of their wins and losses, are more-or-less standings. They order teams approximately according to win-loss percentage but with some attention to how many games each team played. For example, an undefeated team that has played more games is rated higher than an undefeated team that has played fewer. The formula is:

```              WINS - LOSSES
SIMPLE = ---------------
1 + GAMES
```
My motivation for developing this was simple: with the comparisons we are doing of different ranking systems, I wondered how simple standings would stack up.

I complicate this by additionally calculating a "second order" version, as follows:

```
AVERAGE1 = average of the SIMPLE ratings of all opponents,
each weighted by number of games played with
that opponent.

WINS - LOSSES
SIMPLE2 = --------------- + AVERAGE1
1 + GAMES

```

The "third order" Simple rating is:

```
AVERAGE2 = average of the SIMPLE2 ratings of all opponents,
each weighted by number of games played with
that opponent.

WINS - LOSSES
SIMPLE3 = --------------- + AVERAGE2
1 + GAMES

```

I also calculate a fourth order Simple rating analogously, and an "Nth" order rating where I keep repeating the procedure until I figure the returns are diminishing (Actually, to do this, I calculate the 99th order). I've noticed that the ratings do not necessarily converge as the order increases: I recall seeing ratings toggle back and forth between odd and even numbered "orders". I'm guessing non-convergence typically occurs at the beginning of the season when few games are played.

Though the straight (first order) Simple system is too simple to be taken as a literal ranking, the higher order versions of Simple might have some real value in rating and ranking teams.

John Wobus, 1/18/08

Wobus Sports: www.vaporia.com/sports